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3 years ago

Which expression is equivalent to 5a+20? A: 5(5a+4). B: 5(a+4). C: 5(a+20). D: 5(a+1)

Mathematics

1 answer:

guajiro [1.7K]3 years ago

4 0

Answer:

5(a+4)

Step-by-step explanation:

expression is equivalent to 5a+20

To get the equivalent expression we need to factor the given expression

5a+ 20

5a can be written as 5 * a

20 can be written as 5*2*2

WE can see that common factor is 5 for both 5a and 20

So GCF is 5

Now we factor out GCF 5

WE put 5 outside and write all the left of factors inside the parenthesis

5a +20

5 (a+2*2)

5(a+4)

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Find the selling price of a $7.50 agenda book with a 15% discount.

Diano4ka-milaya [45]

Answer:

The selling price of the agenda book is $6.38 to the nearest cent.

Step-by-step explanation:

Assume that the cost price of the agenda book is 100%

∵ The discount is 15%

∵ The selling price = the cost price - discount amount

∴ The selling price = 100% - 15%

→ That means the selling price is 85% of the cost price

∵ The cost price = $7.50

∴ The selling price = 85% × 7.50

→ Change 85% to a number by divide it by 100

∴ The selling price = $\frac{85}{100}$ × 7.50

∴ The selling price = 6.375

→ Round it to the nearest cent (2 d.p)

∴ The selling price = $6.38

∴ The selling price of the agenda book is $6.38 to the nearest cent.

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2 years ago

Plot the four points on the number line below <br> -1/3 1 2/3 2/3 1 1/3

navik [9.2K]

Answer:

Step-by-step explanation:

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3 years ago

The producer of a certain bottling equipment claims that the variance of all its filled bottles is .027 or less. A sample of 30

o-na [289]

Answer:

$p_v = P(\chi^2_{29}>42.963)=1-0.954=0.0459$

b. between .025 and .05

Step-by-step explanation:

Previous concepts and notation

The chi-square test is used to check if the standard deviation of a population is equal to a specified value. We can conduct the test "two-sided test or a one-sided test".

$\bar X$ represent the sample mean

n = 30 sample size

s= 0.2 represent the sample deviation

$\sigma_o =\sqrt{0.027}=0.164$ the value that we want to test

$p_v$ represent the p value for the test

t represent the statistic

$\alpha=$ significance level

State the null and alternative hypothesis

On this case we want to check if the population standard deviation is less than 0.027, so the system of hypothesis are:

H0: $\sigma \leq 0.027$

H1: $\sigma >0.027$

In order to check the hypothesis we need to calculate the statistic given by the following formula:

$t=(n-1) [\frac{s}{\sigma_o}]^2$

This statistic have a Chi Square distribution distribution with n-1 degrees of freedom.

What is the value of your test statistic?

Now we have everything to replace into the formula for the statistic and we got:

$t=(30-1) [\frac{0.2}{0.164}]^2 =42.963$

What is the approximate p-value of the test?

The degrees of freedom are given by:

$df=n-1= 30-1=29$

For this case since we have a right tailed test the p value is given by:

$p_v = P(\chi^2_{29}>42.963)=1-0.954=0.0459$

And the best option would be:

b. between .025 and .05

6 0

3 years ago

can anyone help me with these? I'm having a lot of trouble and I'm extremely behind... I need to catch up badly!!! i have been a

TiliK225 [7]

Answer:

Step-by-step explanation:

5 and 6 are the same, so I will do one of those and you can use the example to do the other one.

Slope-intercept form is y = mx + b. If we have 2 points and nothing else, we can use those 2 points in the slope formula to find the slope (the m value in the equation) and then plug that in with either one of the points to get the equation. The slope formula is:

$m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }$

Using our points in question 5: (2, 4) (5, 4)

$m=\frac{4-4}{5-2} =\frac{0}{3}=0$ So m = 0. Now pick a point and use it in the equation along with the m value to solve for b. I will use (2, 4):

4 = 0(2)+b and

4 = 0 + b so

b = 4.

Now we have m = 0 and b = 4 so we fill in the equation with that info:

y = 0x + 4 or simplifying,

y = 4

For question 7 they want the line parallel to y = 3x + 6 that goes through (-10, 2.5). For a line to be parallel to another line, their slopes have to be identical. The slope in y = 3x + 6 is 3. So the slope of the "new" line is going to be 3 as well. Now we will use that slope and the given point to solve for b, just like in #5:

2.5 = 3(-10) + b and

2.5 = -30 + b so

b = 32.5

Now we will fill in:

y = 3x + 32.5

For question 8 they want the line perpendicular to y = -4x - 2 that goes through (-16, -11). For a line to be perpendicular to another line, their slopes have to be opposite reciprocals. Opposite meaning the sign is opposite (positive becomes negative and negative becomes positive), and reciprocal meaning the fraction is flipped upside down. The slope in our line is -4. That means that the perpendicular slope is positive 1/4. Using that along with our point, we will again solve for b:

$-11=\frac{1}{4}(-16)+b$ which simplifies to

-11 = -4 + b so

b = -7

Now we fill in:

$y=\frac{1}{4}x-7$

For question 8, in order to find the line parallel to the given line, you need to know the slope. In the form it is currently in, we do not know the slope. We need to put it into slope-intercept form to find the slope, then we will proceeed as above. If

x + 4y = 6, then

4y = -x + 6 and, dividing by 4,

$y=-\frac{1}{4}x+\frac{3}{2}$